Hi David,
If the projector is just displaying a black screen, it's possible that your tablet simply doesn't have enough processing and graphics power to send the display over to your projector. I would check to see if your tablet at least has Android 4.4.2 on it. Google states that's the oldest version that will be able to cast its screen. Try connecting it to another source, such as a TV or an old monitor with VGA connectors. If those work and the projector does not, then it could be something with the projector that needs set or isn't compatible with the tablet.
Best of Luck,
Drew.